On the basis of recent state-of-the-art ab initio calculations of the interatomic potential and dipole surface of interacting helium (He) and hydrogen (H) atoms, we calculate the collision-induced absorption spectra in the infrared of the He-H pair, using a rigorous quantum mechanical formalism. Furthermore, we present a simple analytical model which is capable of reproducing these calculated spectra with precision, for frequencies from 50 to roughly 10,000 cm~1 and temperatures from 1500 to 10,000 K. For a given temperature and frequency, the ratio of the absorption coefficient and the product of the H and He densities may be evaluated in seconds, even on small computers (e.g., PCs), provided this ratio exceeds a certain (very small) lower numerical limit.